Method and apparatus for micro-machined sensors using enhanced modulated integrative differential optical sensing

ABSTRACT

Method and apparatus for sensing the displacements of micromachined devices and sensors. The method is referred to as the enhanced modulated integrative differential optical sensing (EMIDOS). The target micromachined proof-mass, for which displacements are measured, includes a grid of slits. The micromachined device is bonded to a CMOS chip containing a matching photodiodes array and their readout electronics. The grid is aligned with the photociiodes. An illumination source, such as an LED, is then mounted above the micromachined device. A model for the noise equivalent displacement (NED), including mechanical, electrical and optical domains, as well as all noise sources is derived. The model predicts that displacements below 10 −3  [√{square root over ( )}Hz] can be measured. The design comprises innovative inertial sensors, an accelerometer and a rategyroscope employing the EMIDOS. Performance models for the noise equivalent acceleration (NEA) and noise equivalent rate (NER) are also derived. The models show that an accelerometer with a very low NEA can be realized.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is related to Israel Patent Application No.122,947, filed Jan. 15, 1998, entitled “Micro-electro-opto-mechanicalinertial sensor with integrative optical sensor” which is assigned tothe co-assignees of the present patent application and is incorporatedherein by reference.

The present application claims priority of Israel Patent Application No.139695 filed 15 Nov. 2000, assigned to the co-assignees, and entitled“METHOD AND APPARATUS FOR MICRO-MACHINED SENSORS USING ENHANCEDMODULATED INTEGRATIVE DIFFERENTIAL OPTICAL SENSING”.

FIELD OF THE INVENTION

The present invention relates generally to sensing the motion ofmicro-machined devices, and specifically to sensing sub-picometer rangemotion in inertial grade gyroscopes and accelerometers.

BACKGROUND OF THE INVENTION

For several decades microelectronics progressed in decreasing size whilesimultaneously increasing complexity. Mechanical structures can now befabricated to comparable dimensions, and can be highly integrated withthe electronics into microelectromechanical systems (MEMS).

MEMS can now be realized as sensors, actuators or mechanical structures.Products using MEMS are used in such life-saving devices as airbagaccelerometers and disposable blood-pressure transducers to monitor theheart rate. MEMS devices have become more complex, and have incorporatedan increasing number of features, progressing from components toelectronic systems. The trend is measured in terms of the level ofintegration of MEMS mechanic and electronics.

The motion of the micro mechanical elements in micro-sensors isgenerally proportional to a particular physical measurement of interest,such as acceleration or partial pressure. Therefore it is important tosense this motion, in-order to reproduce the physical measure. Indevices of more general application, the motion sensing may be used forfeedback control, for example, to restore the micro-machined device toits original physical location. In high-grade sensors, such as inertialgrade gyroscopes and accelerometers, as well as high-grade microphones,the sensing of motion in the sub-picometer (pm) range is required.Moreover, the motion sensing apparatus, itself, should be small andintegrative, in-order to function effectively in the dimensions of themicro-machined devices.

Although the same laws of physics apply in three-dimensional structures,in the micron and sub-micron scales, nonlinear effects that aregenerally negligible in the macro-environment become more significance.Generally, micro-machined proof-masses can move in six degrees offreedom: three along linear axes: x,y and z; and three angles ofrotation about these axes.

The main factor that limits the minimum detectable displacement is thenoise sources that sensing systems are susceptible to. Spurious noisesources include mechanical noise, electrical noise, light noise, etc.Noise sources can be either “white” noise, that is frequencyindependent, or frequency dependent, for example “1/f” noise that isinversely dependent on frequency.

Many motion sensing techniques are known in the art of micro-machinedsensors and devices, as described in the following backgroundreferences:

-   [1] J. A. Plaza, H. Chen, J. Esteve and E. Lora-Tamayo, “New bulk    accelerometer for triaxial detection”, Sensors and Actuators A:    Physical, Vol. 66, 1998, pp. 105–108.-   [2] R. Voss, K. Bauer, W. Ficker, T. Gleissner, W. Kupke, M.    Rose, S. Sassen, J. Schalk, H. Seidel and E. Stenzel, “Silicon    angular rate sensor for automotive applications with piezoelectric    drive and piezoresistive read-out”, Proc. of Transducers'97,    Chicago, 16–19 Jun. 1997, pp. 879–882.-   [3] Y. Nemirovsky, A. Nemirovsky, P. Murlat and N. Setter, “Design    of a novel thin-film piezoelectric accelerometer”, Sensors and    Actuators A: Physical, Vol. 56, 1996, pp. 239–249.-   [4] B. E. Boser and R. T. Howe, “Surface micromachined    accelerometers”, J. of Solid-State Circuits, Vol. 31, No. 3, March    1996, pp. 366–375.-   [5] M. Weinberg, J. Connelly, A. Kourepenis and D. Sargent,    “Microelectromechanical instrument and systems development at the    Charles Stark Draper Laboratory, INC.”, Proceedings of the IEEE    Digital Avionics Systems Conference, 1997, pp. 8.5–33–8.5–40.-   [6] H. K. Rocksatd, T. W. Kenny, J. K. Reynolds, W. J. Kaiser    and T. B. Gabrielson, “A miniature high-sensitive broad-band    accelerometer based on electron tunneling transducers”, Sensors and    Actuators A: Physical, Vol. 43, 1994, pp. 107–114.-   [7] R. L. Kubena, D. J. Vickers-Kirby, R. J. Joyce and Frederick P.    Stratton, “A new tunneling based sensor for inertial rotation rate    measurements”, JMEMS, Vol. 8, no. 4, December 1999, pp. 439–447.-   [8] U. A. Dauderstadt, P. H. S. de Vries, R. Hiratsuka and P. M.    Sarro, “Silicon accelerometer based on thermopiles”, Sensors and    Actuators A: Physical, Vol. 46–47, 1995, pp. 201–204.-   [9] O. Degani, “Investigation of Microelectromechanical Systems    employing Modulated Integrative Differential Optical Sensing”, M.    Sc. Thesis, Supervised by Y. Nemirovsky, Technion, 1999.-   [10] T. Storgaard-Larsen, S. Bouwstra and O. Leistiko,    “Opto-mechanical accelerometer based on strain sensing by bragg    grating in a planar waveguide”, Sensors and Actuators A: Physical,    Vol. 52, 1996, pp. 25–32.-   [11] G. Schopfer, W. Elflein, M. de Labachelerie, H. Porte and S.    Ballandras, “Lateral optical accelerometer micromachined in (100)    silicon with remote readout based on coherence modulation”, Sensors    and Actuators A: Physical, Vol. 68, 1998, pp. 344–349.-   [12] T. B. Gabrielson, “Mechanical-Thermal Noise in Micromachined    Acoustic and Vibration Sensors”, IEEE Trans. On Elec. Dev., Vol. 40,    No. 5, May 1993.-   [13] M. Bao, H. Yang, H. Yin and S. Shen, “Effects of electrostatic    forces generated by the driving signal on capacitive sensing    devices”, Sensors and Actuators A: Physical, Vol. 84, 2000, pp.    213–219.-   [14] S. P. Timoshenko, I. N. Goodier, Theory of Elasticity,    McGraw-Hill, New-York, 1970.-   [15] D. D. Lynch, “Coriolis vibratory gyros”, Proc. of GYRO    technology symposium, Stuttgart, Germany, 15–16 Sep. 1998, pp.    1.0–1.14.

As described in the above references, the known motion sensingtechniques using micro-machined sensors and devices include:piezoresistive [1,2], piezoelectric [3], capacitive [4,5], tunneling[6,7], thermal [8] and optical [9-11] sensing. Few methods have shownthe capability for sensing motions in the sub-picometer range.

The most sensitive method, so far, is based on the tunneling effectbetween a sharp tip and a facing electrode. It has been showntheoretically [12] that the Noise Equivalent Displacement (NED) of thismethod, at the medium frequencies range, is in the order of10⁻²–10⁻³[pm/√Hertz] (10⁻⁴–10⁻⁵[_/√Hertz]) (Hz). Nevertheless, thetunneling effect suffers from inherent “1/f” noise, up to the range of afew Kilohertz (KHz), and its apparatus is quite difficult to realize.Moreover, due to the close proximity required between the tip and thefacing electrode, of the order of a few _ (Angstrom units), the sensingis adversely affected by a relatively high damping coefficient and thusa high thermal-mechanical noise.

Another technique, which is the one most commonly used in micro-machineddevices, and which have shown to be sufficiently sensitive, iscapacitive sensing. This method is rather simple to realize and ishighly integrable. Capacitive sensing does not suffer from inherentnoise sources. The noise of the capacitive transducer is mainlycontributed by the electronic readout circuits or by thermal-mechanicalnoise. Therefore, by proper design of the electronic readout, capacitivesensing is limited only by thermal-mechanical noise, and theoretically aNED of 10⁻²[pm/√Hz] (10⁻⁴[_/√Hz]) can be achieved.

Capacitive sensing, on the other hand, suffers from possible cross talkwith the electronic readout signals, which may exert a parasitic forceon the device [13]. Moreover, without proper shielding it may sufferfrom Electromagnetic Interference (EMI). Due to the close proximitybetween the capacitor plates, which is required to achieve highsensitivity, the capacitive transducer is subjected to a rather highdamping coefficient, which results in a higher thermal-mechanical noise.To lower the damping, vacuum encapsulation is usually required forhigh-grade sensors.

More recently, a piezoresistive configuration with a high degree ofsymmetry was reported to yield a NED in the order of a few [pm/√Hz],which is not quite low enough, but is rather near to the order required[14]. The piezoresistive method is quite easy to realize, and integrate,and was one of the first sensing methods to be used in micro-sensors.Moreover, it does not require close proximity between surfaces, andthus, benefits from a low damping coefficient and low thermal-mechanicalnoise. Nevertheless, it suffers from a high temperature coefficient,which limits the micro-sensor's performance.

Certain aspects of this problem are addressed in the above-referencedco-pending Israeli Patent Application No. 122,947, which is assigned tothe assignees of the present patent application and discloses a viablesystem to sense sub-angstrom displacements. As with the capacitivemethod, MIDOS [9] does not suffer from inherent 1/f noise. As animprovement over capacitive methods, MIDOS is neither susceptible to EMInor to cross talk from readout circuits. The integration of the motionsensing elements, the photodiodes, and the readout electronics on thesame chip also reduces the system noise. Moreover, the sensing is basedon in-plane motion, and close proximity is not required between themechanical elements. Thus, the damping coefficient is lower, and thethermal-mechanical noise, also, is at lower vacuum levels than thoserequired for the capacitive transducer. Nevertheless, the NED of theMIDOS technique is still far from achieving the demands of high-gradesensors.

No other sensing technique has as yet shown a NED lower than 1[pm/√Hz].

Thus there is a need for a micro-machined sensor capable of detectingmotion in the sub-picometer range, and without the drawbacks of priorart devices.

SUMMARY OF THE INVENTION

Accordingly, it is a principal object of the present invention toovercome the limitations of existing micro-machined motion sensingsystems, and to provide improved methods and apparatus for measurementof the motion of high-grade micro-machined devices.

It is a further object of some aspects of the present invention toprovide improved methods and apparatus for an optically based motionsensing method [9], referred to as the Enhanced-Modulated IntegrativeDifferential Optical Sensing (E-MIDOS).

It is a still further object of some aspects of the present invention toprovide improved methods and apparatus for an optically based motionsensing method that is not subject to cross talk with the readoutcircuits and to EMI.

In accordance with a preferred method of the present invention, there isprovided a method for an enhanced version of the MIDOS concept, referredto as E-MIDOS. By using this method the NED can be pushed towards to thesub-picometer range and down to 10⁻¹[pm/√Hz] (10⁻³[_/√Hz]) limit. Thisallows the design of high-grade sensors employing all of the advantagesof the MIDOS concept.

In accordance with a preferred embodiment of the present invention,there is provided a system for micro-machined sensors usingenhanced-modulated integrative differential optical sensing, comprising:

-   a fixed frame;-   a CMOS chip comprising at least two integrated arrays of photodiodes    and analog readout electronics;-   an excitation proof-mass, elastically suspended by beams to said    fixed frame;-   a grid centered along the width of said excitation proof-mass;-   a sensor proof-mass, elastically suspended at right angles to said    excitation proof-mass by beams; and-   a second grid fixed to the frame of said excitation proof-mass, and    added below said first grid, so as to substantially cover the slits    of the first grid.

In some preferred embodiments of the present invention, part integrationmode of E-MIDOS is implemented.

In an alternative embodiment of the present invention, full integrationmode of E-MIDOS is implemented.

Additional features and advantages of the invention will become apparentfrom the following drawings and description.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the invention with regard to theembodiments thereof, reference is made to the accompanying drawings, inwhich like numerals designate corresponding elements or sectionsthroughout, and in which:

FIG. 1 a is a 3-dimensional schematic illustration of a micro-machinedsensor microsystem employing MIDOS, in accordance with the prior art;

FIG. 1 b is a schematic illustration of the cross-section of amicro-machined sensor microsystem employing MIDOS, in accordance withthe prior art;

FIG. 2 a is a 3-dimensional schematic illustration of a micro-machinedsensor's microsystem employing E-MIDOS in part integration mode, inaccordance with an exemplary embodiment of the present invention;

FIG. 2 b is a schematic illustration of the cross-section of amicro-machined sensor's microsystem employing E-MIDOS in partintegration mode, in accordance with an exemplary embodiment of thepresent invention;

FIG. 3 a is a 3-dimensional schematic illustration of a micro-machinedsensor's microsystem employing E-MIDOS in a full integration mode, inaccordance with an exemplary embodiment of the present invention;

FIG. 3 b is a schematic illustration of the cross-section of amicro-machined sensor's microsystem employing E-MIDOS in a fullintegration mode, in accordance with an exemplary embodiment of thepresent invention;

FIG. 4 a is a graph of the TNED at low frequencies vs. the naturalfrequency, illustrating the optical and mechanical dominant regions, inaccordance with an exemplary embodiment of the present invention;

FIG. 4 b is a graph of the TNED at low frequencies vs. the naturalfrequency, illustrating the dominant thermal-mechanical noise, inaccordance with an exemplary embodiment of the present invention;

FIG. 5 is a simplified representation of a lumped physical model(mass-spring-damper) illustrating an accelerometer, in accordance withan exemplary embodiment of the present invention;

FIG. 6 a is a graph of the TNEA of the accelerometer vs. the naturalfrequency, for different gamma factors, in accordance with an exemplaryembodiment of the present invention;

FIG. 6 b is a graph of the TNEA of the accelerometer vs. the naturalfrequency, for different damping ratios factors, in accordance with anexemplary embodiment of the present invention;

FIG. 7 is a schematic illustration of an accelerometer employingE-MIDOS, in accordance with an exemplary embodiment of the presentinvention;

FIG. 8 a is a graph of a design chart for an accelerometer in thesuspensions' length and width phase plane, in accordance with anexemplary embodiment of the present invention;

FIG. 8 b is a graph of the relation between the TNEA and naturalfrequency for an accelerometer, in accordance with an exemplaryembodiment of the present invention;

FIG. 9 is a simplified representation of a lumped physical model(mass-spring-damper) illustrating a decoupled mode CVG, in accordancewith an exemplary embodiment of the present invention;

FIG. 10 a is a graph of the TNER vs. the normalized excitation frequencyfor different gamma factors, in accordance with an exemplary embodimentof the present invention;

FIG. 10 b is a graph of the TNER vs. the normalized excitation frequencyfor different zeta factors, in accordance with an exemplary embodimentof the present invention;

FIG. 10 c is a graph of the TNER vs. the natural frequency for aconstant excitation amplitude, in accordance with an exemplaryembodiment of the present invention;

FIG. 11 is a schematic illustration of a rate-gyroscope employingE-MIDOS, in accordance with an exemplary embodiment of the presentinvention;

FIG. 12 a is a graph of a design chart for the rate-gyroscopeillustrating the sensing mode suspensions length vs. the requirednatural frequency for various suspensions widths, the bold dots arederived from finite element results, in accordance with an exemplaryembodiment of the present invention;

FIG. 12 b is a graph of a design chart for the rate-gyroscopeillustrating the excitation mode suspensions length vs. the requirednatural frequency for various suspensions widths, the bold dots arederived from finite element results, in accordance with an exemplaryembodiment of the present invention;

FIG. 12 c is a graph of the relation of the TNER of the rate-gyroscopeat no-split vs. the natural frequency, in accordance with an exemplaryembodiment of the present invention;

FIG. 13 a is a schematic illustration of the first of three modes of therate-gyroscope case study derived from finite element results, i.e., theoutput sensing mode, in accordance with an exemplary embodiment of thepresent invention;

FIG. 13 b is a schematic illustration of the second of three modes ofthe rate-gyroscope case study derived from finite element results, i.e.,the excitation mode, in accordance with an exemplary embodiment of thepresent invention;

FIG. 13 c is a schematic illustration of the third of three modes of therate-gyroscope case study derived from finite element results, i.e.,with typical natural frequency at least 5 times higher than either thesensing mode or the excitation mode, in accordance with an exemplaryembodiment of the present invention;

FIG. 14 is a schematic illustration of the fabrication process of theinertial-sensors; (a) silicon on insulator (SOI) starting wafer; (b)metal evaporation and patterning; (c) upper silicon patterning usingdeep reactive ion etching (DRIE); (d) handle silicon patterning and (e)device release using HF wet etching of remaining SiO₂, in accordancewith an exemplary embodiment of the present invention;

FIG. 15 is a graph representing the measured photocurrent noise spectraldensity vs. photocurrent for different illumination powers provided by ared light emitting diode (LED) used in the microsystem, in accordancewith an exemplary embodiment of the present invention;

FIG. 16 is a graph representing the measured spectral responses ofphotodiodes with different optical window width. The photodiodes werefabricated in a standard CMOS process provided by Orbit via the MOSISproject, in accordance with an exemplary embodiment of the presentinvention;

FIG. 17 a is a graph representing the effect of diffraction on thesensing of the displacement using EMIDOS, showing the diffractionpatterns at the photodiodes plane for various distances, dz, between thegrid and photodiodes, in accordance with an exemplary embodiment of thepresent invention; and

FIG. 17 b is a graph representing the effect of diffraction on thesensing of the displacement using EMIDOS, showing the differentialresponse of the photodiodes taking into account the diffraction patternvs. the grid displacement, and exhibiting very good linearity at smalldisplacements with only slight non-linearity at large dz's and largedisplacements of the grid, in accordance with an exemplary embodiment ofthe present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Reference is now made to FIG. 1, which is a 3-dimensional schematicillustration of a micro-machined sensor microsystem employing the MIDOSmethod 20, in accordance with the prior art.

The apparatus is constructed from three main parts: an illuminationsource 22, in the form of a light-emitting diode (LED); a micro-machinedsuspended proof-mass 24 and a CMOS chip including photodetectors, suchas photodiodes 30, and their readout electronics. The micro-machineddevice 18, a mechanical part, is flip-chip bonded to the CMOS chip 26using indium bumps 28 technology. Proof-mass 24 is aligned with twophotodiodes 30 a and 30 b, such that when no induced displacement isapplied, an equal portion of photodiodes 30 a and 30 b is covered. Theelectronic readout 32 subtracts and amplifies the resultingphotocurrents readout from photodiodes 30.

FIG. 1 b is a schematic illustration of the cross-section of amicro-machined sensor microsystem employing MIDOS method 32, inaccordance with the prior art. The MIDOS principle of operation isshown. Two views of microsystem 32 are shown: 32 a is before a lineardisplacement 34 takes place; 32 b is after linear displacement 34 takesplace. When a linear displacement signal along the x-axis is induced,the uncovered portion of one photodiode 30 a increases, while theuncovered portion of photodiode 30 b decreases by the same amount.Thereupon, a differential photocurrent is electronically amplified,resulting in an electrical signal proportional to displacement 34.

The noise equivalent displacement (NED) of a microsystem employing theMIDOS method is given by

$\begin{matrix}{S_{x} = \frac{q\; W_{D}}{L_{D}I_{\lambda}R}} & (1)\end{matrix}$where L_(D) and W_(D) 34 are the length and width of the photodiodes 30,respectively, q is the electron charge, R is the responsivity ofphotodiodes 30 and I_(□) the illumination intensity at the plane ofphotodiodes 30. Thus, longer and narrower photodiodes 30 improve the NEDand also provide higher illumination intensity.

The E-MIDOS Principle

FIGS. 2 a and 3 a are alternate embodiments of a micro-machined sensor'smicrosystem employing E-MIDOS 40.

FIG. 2 a is a 3-dimensional schematic illustration of a micro-machinedsensor's microsystem employing E-MIDOS in part integration mode 40 a, inaccordance with an exemplary embodiment of the present invention. Theapparatus of microsystem includes the same three parts of MIDOSmicrosystem 20. Nevertheless, three main features differentiate E-MIDOSsystems 40 from MIDOS 20 method:

-   (1) Photodiodes 30 are relocated in the center of proof-mass 24    rather than on the sides.-   (2) Two photodiodes 30 are replaced with two arrays of photodiodes    42.-   (3) Proof-mass 24 includes a matching grid 44 to photodiodes arrays    42.    The electronic readout 32 takes a summation by integration of the    photocurrents of each array of photodiodes 42 and then subtracts and    amplifies the resulting pair of summed electrical signals.

FIG. 2 b is a schematic illustration of the cross-section of amicro-machined sensor's microsystem employing E-MIDOS in partintegration mode 40 a, in accordance with an exemplary embodiment of thepresent invention. Similarly to MIDOS 20 method, when a displacement isinduced, the uncovered (illuminated) area of one array of photodiodes 42a is increased, while the uncovered area of the second array 42 bdecreases. Thus, an electrical signal proportional to the displacementis recorded at the output of electronic readout 32.

Before proceeding with a more quantitative evaluation of the improvementin the NED using the E-MIDOS method 40, qualitative considerations aresummarized as follows:

-   (1)The use of photodiodes' arrays 42 increases the effective length    compared to that of pair of photodiodes 30. Thus, the average value    of the displacement signal is increased and the NED is reduced.-   (2)The use of a stack grid in proof-mass 24 forces the effective    width of photodiodes arrays 42 to be reduced, and therefore reduces    the noise.-   (3)The relocation of photodiodes arrays 42 in the center of    proof-mass 24 allows using the center of the illumination spot 46    rather than the tails. The illumination intensity is greater at the    center, and thus reduces the NED. Moreover, by using this    configuration illumination spot 46 can be concentrated to the area    of photodiodes arrays 42, thus increasing the illumination    intensity, and therefore further improving the NED.

FIG. 3 a is a 3-dimensional schematic illustration of a micro-machinedsensor's microsystem employing E-MIDOS in a full integration mode 40 b,in accordance with an exemplary embodiment of the present invention. Inpart integration configuration 40 a photodiodes arrays 42 were partiallycovered by the slit edge, and therefore the illumination 46 crossing theslit is partially collected and therefore included in the integration byarrays of photodiodes 42, and thus the name. In full integration modeconfiguration 40 b photodiodes 42 are underlying each slit, thuscollecting (integrating) all the illumination 46 that crosses the slit.The main difference between the two modes is that a second grid 44 b isadded covering the interstices of the first grid 44 a. Second grid 44 bis fixed to the frame of suspended proof-mass 24, and thus does not movewith first grid 44 a.

FIG. 3 b is a schematic illustration of the cross-section of amicro-machined sensor's microsystem employing E-MIDOS in a fullintegration mode 46 b, in accordance with an exemplary embodiment of thepresent invention. As a displacement is induced on the moving grid (i.e.the suspended proof-mass 24), the slits on one side of fixed grid 44 bbecome narrower while on the other side become wider. Thus, the totalillumination crossing the slits, and collected by arrays of photodiodes42 underlying them, decreases on one side, while increasing on the otherside of the fixed grid. By using the same electronics readout 32 theresult is an electrical signal proportional to displacement 34.

The advantage of full-integration mode 40 b over part-integration mode40 a is in better linearity. Since in part-integration mode 40 a onlypart of illumination 46 crossing each slit is collected, the transferfunction from displacement to photocurrent on the photodiode is highlydependent on the specific illumination pattern over the slit. Thusdiffraction effects, if dominant, may cause the transfer function to benon-linear. For full-integration mode 40 b all illumination 46 crossingthe slit is collected by photodiode arrays 42, thus the transferfunction is independent of the diffraction pattern. The illuminationcrossing the slit is linearly proportional to the slit width andtherefore also the signal. The main drawback of full-integration mode 40b is its fabrication complexity. Thus, only when very narrow slits areto be used, where diffraction effects take a more dominant role, shouldfull-integration mode 40 b be used.

An Optoelectromechanical Model

Hereinbelow is derived a quantitative model for the output electricalsignal of E-MIDOS microsystem 40 vs. input displacement 34 of theproof-mass 24. All noise sources of an integrated microsystem employingE-MIDOS 40 are discussed and a model for the NED of the microsystem 40is also derived.

The Optoelectromechanical Transfer Function

The optical analysis of the microsystem 40 is based on the paraxial rayoptics approximation. FIGS. 2 b and 3 b contain the dimensionaldefinitions required for the analysis described hereinbelow. The use ofthe paraxial ray optics approximation is not straightforward, and thediffraction limitation is considered in several cases. A more detaileddiscussion of the diffraction limitation and its influence is given inAppendix A.

Nevertheless, as long as the slit width 52, W_(S), is large compared tothe illumination wavelength, λ, and the gap to the photodiodes, d, andthe photodiodes nominal width 36, W_(D), is fitted as well, thediffraction limitation can be neglected in part integration mode 40 a.It should be emphasized that even if the above conditions do notprevail, the operating principle remains unchanged, because the responsebecomes non-linear for large displacements 34 (x).

In full-integration mode 40 b the diffraction does not set any limit andparaxial optics can be used as long as photodiode width 36 is largeenough to collect most of the illumination. It should be noted that asslit width 52 becomes smaller compared to the gap to the photodiodes,the diffraction effect is enhanced and the ratio of photodiode width 36to nominal slit width 52 should be increased to collect the illuminationproperly. All of the above factors set some limitation on the minimumNED possible to sense using the E-MIDOS method.

Using the definitions described in FIGS. 2 b and 3 b and paraxial rayoptics, and assuming a linear displacement of δx, the resultingphotocurrent signal after subtraction, δi, is given byδi=2nI_(λ)RL_(D)δx  (2)where n is the number of photodiodes pairs 58, I_(□) the illuminationintensity, R the photodiodes' responsivity and L_(D) the photodiodes'length. This formula for δi is known as the transfer function of theopto-mechanical part.

It should be emphasized that the above relation is given for the currentconfiguration of photodiode arrays 42. Other configurations may bechosen for measuring multi-axial, linear or angular displacements, whichmay result in a slightly different relation.

The Noise Sources

Now all the noise sources related with E-MIDOS microsystem 40 areconsidered. The noise model is necessary for the design considerationsof system 40. The main factor that limits the minimum detectabledisplacement is the noise sources that sensing systems are susceptibleto. Spurious noise sources include mechanical noise, electrical noise,light noise, etc. Noise sources can be either “white” noise, that isfrequency independent, or frequency dependent, for example “1/f” noisethat is inversely dependent on frequency.

The illumination source may be modulated if low frequency signals are tobe resolved, thus eliminating the contribution of the electronics' 1/fnoise. Therefore, throughout the following discussion the 1/fcontribution will be neglected.

Electronics Noise

A typical electronics readout circuitry 32 is divided into two stages, atransimpedance amplification stage for each of the two photodiodes'arrays 42 and a subtraction stage. The input referred current noisespectral density of exemplary electronics readout circuitry 32 was shownto be

$\begin{matrix}{S_{I}^{elec} = \frac{8\; k_{B}T}{R_{f}}} & (3)\end{matrix}$where k_(B) is the Boltzman constant, T is the temperature in degreesKelvin and R_(f) is the transimpedance stage feedback resistor andamplification. Throughout the derivation of the input referred noise thecontribution of the amplifiers noise is neglected, since ultra-low noiseamplifiers are preferably used.

The displacement referred noise of the electronics readout 32 iscalculated using relations (2) and (3), and its spectral density isgiven by

$\begin{matrix}{S_{x}^{elec} = {{S_{1}^{elec} \times {\frac{\delta\; x}{\delta\; i}}^{2}} = \frac{2k_{B}T}{n^{2}I_{\lambda}^{2}R^{2}L_{D}^{2}R_{f}}}} & (4)\end{matrix}$

Thermal-Mechanical Noise

Now consider the thermal-mechanical noise in exemplary system 40 withone unconstrained degree of freedom, which is a good generalrepresentation. A simplified mass-spring-damper representation of thesystem 70 is shown in FIG. 5. The equation of motion of such a system isgiven bym{umlaut over (x)}+D{dot over (x)}+Kx=F  (5)where m is the mass of proof-mass 24, D is the damping coefficient, K isthe stiffness coefficient and F the acting force.

Callen and Greene have shown in their fluctuation-dissipation theoremthat an actual spring-mass-damper system can be replaced with an idealone having fluctuating force noise source acting on the mass with aspectral density ofS_(F)=4k_(B)TD  (6)By using the Fourier transform on equation (5), the displacementreferred thermal-mechanical noise spectral density is derived

$\begin{matrix}{{S_{x}^{TM} = {{S_{F}{\frac{x}{F}}^{2}} = {\frac{{8\; k_{B}T}\;}{m} \times \frac{\;{\zeta\;\omega_{n}}}{( {\omega_{n}^{2} - \omega^{2}} )^{2} + {4\zeta^{2}\omega_{n}^{2}\omega^{2}}}}}},} & (7)\end{matrix}$where ω_(n)=√K/m is the natural frequency of system 40, and ζ is thenormalized damping coefficient, where 2ζω_(n)=D/m.

Photodiode Noise

The last noise source to be considered is the photodiode noise. Thephotodiode noise contribution is divided into the saturation (dark)current noise and the photocurrent noise. Assuming that the saturationcurrent is negligible compared to the photocurrent, the photocurrentnoise spectral densityS_(Idiode)=4qI_(L),  (8)where q is the electron charge and I_(L) is the total averagephotocurrent of each of two photodiode arrays 42. Using equations (3)and (8) it can be concluded that as long as I_(L)R_(f)>>2k_(B)T/q, theelectronic noise is negligible compared with the photocurrent noise. Theright hand term of the equation equals ˜0.05[V] at room temperature, andthus by proper choice of the feedback resistor this inequality relationis easily achieved.

Using the geometrical parameters from FIGS. 2 b and 3 b, equation (8)can be rewritten as

$\begin{matrix}{S_{Idiode} = \{ \begin{matrix}{4\; q\; n\; W_{D}L_{D}I_{\lambda}R} & {{part}\text{-}{int}\mspace{14mu}{egration}\mspace{14mu}{mod}\mspace{14mu} e} \\{4\; q\; n\; W_{S}L_{D}I_{\lambda}R} & {{full}\text{-}{int}\mspace{14mu}{egration}\mspace{14mu}{mod}\mspace{14mu} e}\end{matrix} } & (9)\end{matrix}$where W_(D) is nominal photodiode width 36 in part-integration mode 40 aand W_(S) is the nominal slit width 52 in the full-integration mode 40b.

Employing equation (2), the displacement referred photocurrent noisespectral density is given by

$\begin{matrix}\begin{matrix}{S_{x}^{PD} = {\frac{q\;}{P \cdot R}\gamma\mspace{20mu}{and}}} \\{{\gamma = \frac{{AW}_{({D\mspace{14mu}{or}\mspace{14mu} S})}}{n\; L_{D}}},}\end{matrix} & (10)\end{matrix}$where P is the total illumination source power and A is illuminationspot area 46. In the last derivation assume approximately constantintensity over photodiodes illumination area 46.

Optimal spot size 46, which employs the illumination power to themaximum, encloses grid square 44 and thus has an area of

$A = {\frac{\pi}{2}{L_{D}^{2}.}}$Moreover for a large number of photodiode pairs 58 in each grid, n, andassuming square grid n is approximately given by

$n \cong \frac{L_{D}}{W_{P}}$where W_(P) is the period width 60 of the grid. Thus γ is approximatelygiven by

$\begin{matrix}{\gamma \cong {\frac{\pi}{2}W_{P}{W_{({D\mspace{14mu}{or}\mspace{14mu} S})}.}}} & (11)\end{matrix}$

Therefore, conclude that the displacement referred photocurrent noise isindependent of the specific total dimensions of the grid and is onlydependent upon the grid period 60 and the nominal slit (in fullintegration mode 40 b) width 52 or nominal diode (in part integrationmode 40 a) width 36. Thus the grid can be enlarged or reduced in sizeaccording to the restrictions of the optical illumination spot size 46.It is apparent to those skilled in the art, that as long as the grid ismore dense, i.e. lower period width 60 and lower slit width 52 or diodenominal width 36 accordingly, the sensing limitation is improved.

The Total Noise Equivalent Displacement (TNED)

Consideration is now made of the total noise contribution ofmicro-system 40. Assuming that electronic readout circuit 32 is properlydesigned, it is concluded that the total displacement referred noisespectral density is given by

$S_{x}^{Total} = {\frac{q\;\gamma}{P\; R} + {\frac{{8\; k_{B}T}\;}{m} \times {\frac{\;{\zeta\;\omega_{n}}}{( {\omega_{n}^{2} - \omega^{2}} )^{2} + {4\zeta^{2}\omega_{n}^{2}\omega^{2}}}.}}}$For sensors operating below the natural frequency of the mechanicalsystem, such as the accelerometer, the TNED spectral density at lowfrequencies is

$\begin{matrix}{{S_{x}^{Total}❘_{\omega{\operatorname{<<}\omega_{n}}}} = {\frac{q\;\gamma}{PR} + {\frac{8\; k_{B}T}{m} \cdot {\frac{\zeta}{\omega_{n}^{3}}.}}}} & (12)\end{matrix}$

FIG. 4 a is a graph presenting the TNED at low frequencies vs. thenatural frequency, ω_(n) 90, for different damping ratios, ζ, and γfactors and for typical values of P, R and a typical proof-mass 24, m,of a mass-produced micro-machined sensor. The figure exhibits two mainregions: (1) the optical dominant region at natural frequencies above afew hundred hertz 92 and (2) the mechanical dominant region at naturalfrequencies below ˜10[Hz] 94.

In higher frequency region 92, the TNED is dominated mainly by thephotocurrent noise and is only dependent on the γ factor and not thenatural frequency, ω_(n), or the mechanical damping ratio, ζ, of system40. It is apparent to those skilled in the art, that for γ factors lowerthan ˜10[μm²] the TNED is lower than 10⁻³[_/√Hz]. γ factors of a fewtenths to a hundred can be achieved easily with period width 60, W_(P),of a few tenths of microns and diode width 36 or silt width 52 of a fewmicrons, resulting in a TNED only slightly higher.

In lower frequency region 94, the thermal-mechanical noise is the mainnoise source and the TNED increases as the natural frequency is reduced.Nevertheless, since the natural frequency of typical micro-machinedsensors 40 is above 100 [Hz], it is assumed that the TNED is mainlydominated by the photocurrent noise and the correction can be estimatedusing equation (12).

For sensors operating near to the natural frequency of the mechanicalsystem, such as the rate-gyroscope, the TNED can be estimated by

$\begin{matrix}{{S_{x}^{Total}❘_{\omega = \omega_{n}}} = {\frac{q\;\gamma}{PR} + {\frac{2\; k_{B}T}{m} \times {\frac{1}{{\zeta\omega}_{n}^{3}}.}}}} & (13)\end{matrix}$

Thus, the thermal-mechanical noise is increased by the square of thequality factor, Q, where Q=½ζ.

FIG. 4 b presents the TNED at the natural frequency vs. the naturalfrequency, ω_(n) 96, for different damping ratios ζ, and γ factors, andfor typical values of P, R and a typical proof-mass, m, of amass-produced micro-machined sensor 40. Unlike the low frequencies caseabove, in the present case the TNED is dominated by thethermal-mechanical noise over most of the entire range.

Since the typical natural frequencies of micro-machined sensors 40 arein the range of 100[Hz]-10[KHz], at low-frequencies the dominant noisesource is the photocurrent noise while at frequencies near the naturalfrequency the dominant noise source is the thermal-mechanical noise.

The influence of the γ factor on the noise figure at frequencies nearthe natural frequencies is further discussed hereinbelow at the sectionentitled Design of a Rate Gyroscope Using EMIDOS.

Design of an Accelerometer Employing EMIDOS

In what follows the design of a novel accelerometer employing EMIDOS isdiscussed. An accelerometer is a sensor intended for measuring theabsolute acceleration of a body in three dimensional space with respectto an inertial frame of reference.

Many designs of micro-machined accelerometers have been reported so far,with one, two or three axes of sensitivity, employing various sensingmethods, such as: capacitive, piezoelectric, piezoresistive, thermal,electron tunneling, Bragg grating, MOS strain sensitive and optical.

The typical requirements from micro-machined accelerometers are known inthe art for various applications ranging from the automobile industry toinertial navigation. Typical requirements for the automobile applicationare a noise equivalent acceleration (NEA) of ˜1[mg/√Hz] for a bandwidthof 400[Hz], while for inertial navigation the requirements are an NEA of˜1[μg/√Hz] for a bandwidth of 100[Hz].

In the first section hereinbelow, the principle of operation and thedynamic model of a single axis accelerometer are presented. The sectionthereafter discusses the performance, i.e. the TNEA and the bandwidth,of the same accelerometer. Finally, a case study of a micro-machinedaccelerometer employing EMIDOS is presented.

Principle of Operation Based on a Dynamic Model

The dynamic model of a single axis accelerometer micro-system is basedon the mass-spring-damper lumped model 70, which is presented in FIG. 5.The figure presents a physical model of a system having one degree offreedom (DOF). A proof-mass 24, m, is suspended from a solid frame 74via a linear spring 76, K. Damping is represented by a viscous lineardamper 78, which is denoted by D. Due to linear acceleration, a, ofsolid frame 74 along the x axis, a displacement, δx, of proof-mass 24 inopposite direction is generated. This displacement is further detectedby E-MIDOS apparatus 40.

The equation of motion, which relates the linear acceleration and thedisplacement, is derived using Newton's second lawmδ{umlaut over (x)}+Dδ{dot over (x)}+Kδx=−ma.  (14)

The displacement δx is measured relative to a frame of referenceattached to the solid frame and having its origin coinciding with thecenter of mass 82 (cg) when at equilibrium.

Applying the Fourier transform to equation (14) results in:

$\begin{matrix}{\frac{\delta\;\overset{\sim}{x}}{\overset{\sim}{a}} = {- \frac{1}{( {\omega_{n}^{2} - \omega^{2}} ) + {2\;{j\zeta}\;\omega\;\omega_{n}}}}} & (15)\end{matrix}$where ω_(n) and ζ are defined hereinabove.

Performance and Noise Equivalent Acceleration (NEA)

The first parameter of the accelerometer to be discussed is the TotalNoise Equivalent Acceleration (TNEA). The TNEA can be derived using theTNED derivation hereinabove, and equation (15), which relates thedisplacement and induced acceleration. The TNEA spectral density istherefore given by

$S_{a} = {{S_{x} \cdot {\frac{a}{\delta\; x}}^{2}} = {{\frac{q\;\gamma}{PR}\lbrack {( {\omega_{n}^{2} - \omega^{2}} )^{2} + {4\zeta^{2}\omega^{2}\omega_{n}^{2}}} \rbrack} + {\frac{8\; k_{B}T\;\zeta\;\omega_{n}}{m}.}}}$Since the operation range of the accelerometer is at frequencies lowerthan the natural frequency, the TNEA can be approximated in this rangeby

$\begin{matrix}{{S_{a} = {{\frac{q\;\gamma}{PR}\omega_{n}^{4}} + \frac{8\; k_{B}T\;\zeta\;\omega_{n}}{m}}},} & (16)\end{matrix}$where the root mean square (RMS) of the TNEA=√(S_(a)′BW), where BW isthe effective bandwidth of readout electronics 32.Equation (16) relates the TNEA with another major parameter of theaccelerometer, the natural frequency, which relates to the totalbandwidth of the accelerometer. For low damping ratios, ζ, the totalbandwidth is about 55% of the natural frequency ω_(n).

Equation (16) also emphasizes the advantage of bulk micro-machinedaccelerometers. The thermal-mechanical noise is reduced as the mass ofproof-mass 24, m, is increased. Moreover, it is clearly seen that theTNEA is improved as the natural frequency of the sensor is decreased,either being thermal-mechanical noise dominated, or photo-current noisedominated.

FIG. 6 a presents the TNEA of the accelerometer vs. the naturalfrequency, ω_(n), for different γ factors 100. It is clearly shown thatfor given typical parameters, the TNEA is dominated by the photocurrentnoise over the all range of the natural frequencies. The contribution ofthe thermal-mechanical noise is slightly observed at low naturalfrequencies for γ=10[μm²]. It is clearly seen that sub-μg accelerometerscan be easily realized and even accelerometers with a TNEA of a fewng/√Hz can be realized. This is due to the ability to combine highsensitivity with very low thermal-mechanical noise, i.e. low dampingratio, ζ.

FIG. 6 b is a graph of the TNEA of the accelerometer vs. the naturalfrequency, ω_(n), for different damping ratios, ζ 104. This figureexhibits the influence of the thermal-mechanical noise and thedegradation of the TNEA at low natural frequencies due to higherdamping. Nevertheless, sub-μg resolution can be achieved even withhigher damping coefficients.

Design Case Study

In the following, a design case study of an accelerometer employingEMIDOS is discussed. The TNEA and natural frequencies are derived forthe structure, and the design considerations of the accelerometer arediscussed.

FIG. 7 is a schematic illustration of an accelerometer employing E-MIDOS110, in accordance with an exemplary embodiment of the presentinvention. The suspending beams and the grid are assumed withrectangular cross-section, see the Fabrication Process, describedhereinbelow. The total thickness of all the accelerometer mechanicalstructural elements, i.e. beams, proof-mass 24 and grid 44, is denotedby T. Grid 44 is centered with respect to proof-mass 24. It is notedthat grid 44 does not fill entire proof-mass 24 and mass 24 is extendedto fill most of the inner frame. This is done in order to increase thetotal mass and reduce the thermal-mechanical noise. Grid 44 iscircumscribed by, and is not required to be extended over, the entirecircumference of illumination spot 46 as was discussed hereinabove inthe section entitled Photodiode Noise, and shown therewith in FIG. 3 b.

According to the above, the mass and the suspension coefficient of thestructure are given by [14]

$\begin{matrix}\begin{matrix}{m = {\rho\;{T\lbrack {{W_{M}L_{M}} + {{2 \cdot ( {W_{S} + W_{K}} )}( {L_{F} - {2\; L_{K}}} )} - {n\; L_{G}\frac{W_{P}}{2}}} \rbrack}}} \\{K = {4{ET}\frac{W_{K}^{3}}{L_{K}^{3}}}}\end{matrix} & (17)\end{matrix}$where ρ, E are the mass density and Young's modulus of silicon, W_(M)and L_(M) are the proof-mass total width 112 and proof-mass total length114, respectively, W_(K) and L_(K) are the suspension width 116 andsuspension length 118, respectively, W_(F) and L_(F) are the inner width120 and length 122 of the fixed frame, respectively, W_(P) 60 is thegrid period, L_(G) the grid width and length 124, W_(S) 52 is thegeneral spacing between the mechanical elements, n is the number ofslits in the grid. Moreover the following relations prevail

$\begin{matrix}{n = {\frac{L_{G}}{W_{P}} + \frac{1}{2}}} \\{L_{M} = {L_{F} - {2\; W_{S}}}} \\{W_{M} = {W_{F} - {4\; W_{S}} - {2W_{K}}}}\end{matrix}$Thus the natural frequency of the structure can be calculated using

$\begin{matrix}{\omega_{n}^{2} = {\frac{4E}{\rho}\frac{W_{K}^{3}}{\begin{matrix}{L_{K}^{3}\lbrack {{( {W_{F} - {4W_{S}} - {2W_{K}}} )( {L_{F} - {2W_{S}}} )} + {2 \cdot}} } \\ {{( {W_{S} + W_{K}} )\;( {L_{F} - {2L_{K}}} )} - {( {\frac{L_{G}}{W_{P}} + \frac{1}{2}} )L_{G}\frac{W_{P}}{2}}} \rbrack\end{matrix}}}} & (18)\end{matrix}$and the TNEA can be easily evaluated then using equation (16).

FIG. 8 a is a graph of a design chart for an accelerometer in thesuspensions' length and width phase plane 130, in accordance with anexemplary embodiment of the present invention. Equi-potential lines 132of the natural frequency are drawn in the chart for the set ofparameters summarized in Table I below. Using Table I, the length andwidth parameters of the beams, as detailed in FIG. 7, can be set for therequired natural frequency.

TABLE I Parameter Value Inner frame length - L_(f) [μm] 3200 Inner framewidth - W_(f) [μm] 1700 Structure thickness - T [μ] 50 Grid length andwidth - L_(G) [μm] 525 Grid period - W_(P) [μm] 50 Photodiodes nominalwidth - W_(D) [μm] 2.5 General spacing - Ws [μm] 25 Young modulus - E[Pa] 1.31 × 10¹¹    Mass density - ρ [Kg/m³] 2.33 × 10³    Electroncharge - q [Coulomb]  1.6 × 10⁻¹⁹ Illumination source power - P [Watt]10⁻³ Photodiodes responsivity - R [A/W] 0.2 Thermal energy - k_(B)T [eV]0.026

FIG. 8 b completes the abovementioned chart by illustrating the relationbetween the TNEA and natural frequency for the current accelerometerdesign 140. Moreover, FIG. 8 b illustrates the change in the TNEA vs.natural frequency for different damping ratios, ζ, i.e. different vacuumlevels. By choosing the required TNEA, the natural frequency is set, andby referencing FIG. 8 a the geometrical dimensions are completed.

Design of a Rate Gyroscope Employing EMIDOS

In the following section the design considerations of a second inertialsensor, the rate-gyroscope, employing EMIDOS is discussed. A rategyroscope is a sensor used for measuring the rate of rotation (angularvelocity) of a body about a specific body fixed axis.

Micro-machined rate-gyroscopes have a more complex nature than theaccelerometers. Most micro-machined gyroscopes are Coriolis VibratoryGyros (CVG) [15], i.e. based on the Coriolis effect. The Coriolis effectstates that if a body has a velocity V with respect to a rotating (Ω)frame of reference, a force equal to the cross product of the rate ofthe frame and the velocity of the body (Ω×V) is exerted on the body. Atypical micro-machined CVG consists of an elastic body, such that one ofits resonant modes (1) is excited to the constant resonant vibration.Inducing a rotational rate about a particular body-fixed axis, excites adifferent resonant mode (2) into vibration due to the Coriolis effect.The amplitude of the second mode is the measure of the induced rate.

Several actuation methods have been used for driving the first mode (1)into vibration, among which are: electrostatic actuation;electromagnetic actuation; and piezoelectric actuation. The output mode(2) motion has thus far been mainly sensed by either capacitive orpiezoresistive methods, however optical as well as tunneling methodshave also been reported.

The typical requirements for micro-machined rate-gyroscopes are known inthe art, and are divided into three grades: rate grade, tactical gradeand navigation grade. Typical requirements for the rate grade are anoise equivalent rate (NER) of >30[deg/hr/√Hz], for a bandwidth of70[Hz]; for the tactical grade are an NER of >3[deg/hr/√Hz] for abandwidth of 100[Hz], and for the navigation grade an NER of<0.05[deg/hr/√Hz] for a bandwidth of 100[Hz].

In the first section to follow the principle of operation and thedynamic model of a single axis de-coupled mode rate-gyroscope arepresented. The second section discusses the performance, mainly theTNER, of the presented rate-gyroscope. Finally, a case study of amicro-machined rate-gyroscope employing EMIDOS is presented.

Principle of Operation and Dynamic Model of a Single Axis De-coupledMode Rate Gyroscope

FIG. 9 illustrates a lumped physical model (mass-spring-damper) of ade-coupled mode CVG 172. Therein, an inner sensor mass 38 is suspendedvia linear spring 174 and damper 176 to a second outer excitation mass180, which is further suspended via a second set of linear spring 182and damper 184 to a solid frame 186. (x,y,z) is a Cartesian frame ofreference that is fixed relative to the solid frame. The y-axis isperpendicular to the x-z plane 188 of CVG illustration 172. When atrest, the origin of axes coincides with the center of mass of the innermass—cg 190.

The second set of linear spring 182 and damper 184 confine outer mass180 displacements to a linear motion along the z-axis. Inner mass 38 isassumed to move with outer mass 180 along the z-axis, i.e. an infinitestiffness is assumed between the inner and outer masses in thez-direction. The relative displacements of inner mass 38 with respect toouter mass 180 are confined to a linear motion along the x-axis. Theabsolute angular velocity of the solid frame, Ω_(Y), is assumed aboutthe y-axis.

Outer mass 180 is excited into vibrations via an excitation forceF_(exc) 170 in the z-direction. Thus, inner-mass 38 is excited into thesame vibrations as outer mass 180 in the z-direction since they movetogether therewith. Due to angular velocity about the y-axis a Coriolisforce is exterted on both masses in the x-direction. Since onlyinner-mass 38 can move along the x-axis, only inner mass 38 vibrates inthe x-direction as a result of the Coriolis force. These vibrations areresolved by the E-MIDOS and are a measure of the rate.

A thorough analysis of a vibrating rate gyroscope assumes low andconstant rate, whereby the following equations of motion are derived [9]

$\begin{matrix}\begin{matrix}{{{\delta\;\overset{¨}{x}} + {2\zeta_{x}\omega_{n\; x}\delta\;\overset{.}{x}} + {\omega_{n\; x}^{2}\delta\; x}} = {{- 2}\;\Omega_{y}\delta\;\overset{.}{z}}} \\{{{\delta\;\overset{¨}{z}} + {2\zeta_{z}\omega_{n\; z}\delta\;\overset{.}{z}} + {\omega_{n\; z}^{2}\delta\; z}} = \frac{F_{exc}}{m_{exc} + m_{sen}}}\end{matrix} & (19)\end{matrix}$where: δx is the displacement of inner mass 38 along the x-axis of theCartesian frame; δz is the displacement of inner-mass 38 (and outer-mass140) along the z-axis of the Cartesian frame; ω_(nx)=K_(sen)/m_(sen) isthe output natural frequency; ζ_(x)=D_(sen)/(2ω_(nx)′m_(sen)) is theoutput damping ratio; ω_(nz)=K_(exc)/(M_(exc)+m_(sen)) is the excitationnatural frequency; ζ_(z)=D_(exc)/[2ω_(nz)′ (m_(sen)+m_(exc))] is theexcitation damping ratio; and F_(exc) is excitation force 170, which isassumed to be sinusoidal with an excitation frequency denoted by ω.Using the Fourier transform, the following is derived

$\begin{matrix}\begin{matrix}{{{\delta\;\overset{\sim}{x}}} = {\frac{2{\omega\Omega y}}{\sqrt{( {\omega_{n\; x}^{2} - \omega^{2}} )^{2} + {4\;\zeta_{x}^{2}\omega_{n\; x}^{2}\omega^{2}}}}{{\delta\;\overset{\sim}{z}}}}} \\{{{\delta\;\overset{\sim}{z}}} = {\frac{1}{\sqrt{( {\omega_{nz}^{2} - \omega^{2}} )^{2} + {4\;\zeta_{z}^{2}\omega_{n\; z}^{2}\omega^{2}}}}{{\overset{\sim}{a}}_{exc}}}}\end{matrix} & (20)\end{matrix}$where |δ{tilde over (x)}|, |δ{tilde over (z)}| are the output andexcitation amplitudes, respectively, and |ã_(exc)|=|{tilde over(F)}_(exc)|/(m_(exc)+m_(sen)) is the excitation acceleration amplitude.

It is easily derived by one skilled in the art, from equation (20) thatfor a given excitation 170 amplitude the maximal response occurs atω=ω_(nx). For the excitation amplitude it is clearly seen that for lowdamping ratios and constant excitation force amplitude the maximalexcitation amplitude occur at ω≈ω_(nz). Thus, it is obvious that thebest response of the rate-gyroscope is when ω≈ω_(nx)≈ω_(nz).

In order to maintain a constant relation between the output amplitudeand rate, it is highly important to maintain and control the excitationfrequency and excitation amplitude 170 constant. Techniques to achievethis control usually maintain the excitation frequency at the excitationnatural frequency and the excitation amplitude constant. Nevertheless,due to bandwidth requirements and fabrication tolerances, some deviationoccurs in the excitation and output natural frequencies, which resultsin lower output response. It is therefore assumed in the followingderivations that the excitation frequency is the excitation naturalfrequency and that the excitation amplitude is constant and examinationis made of the influence of the deviation occurring in the naturalfrequencies.

The Noise Equivalent Rate (NER)

The total noise equivalent rate (TNER) can be derived using the TNEDderivation from section on Photodiode Noise and equation (20), assumingconstant excitation amplitude, the TNER spectral density is given by,

$\begin{matrix}{S_{\Omega} = {{S_{x}{\frac{\Omega}{x}}^{2}} = {{\frac{q\;\gamma}{P\; R}\frac{( {\omega_{n\; x}^{2} - \omega^{2}} )^{2} + {4\;\zeta_{x}^{2}\omega_{n\; x}^{2}\omega^{2}}}{4\;\omega^{2}{{\delta\;\overset{\sim}{z}}}^{2}}} + \frac{2\; k_{B}T\;\zeta_{x}\omega_{n\; x}}{m_{{sen}\;}\omega^{2}{{\delta\;\overset{\sim}{z}}}^{2}}}}} & (21)\end{matrix}$where the RMS of the TNER=√(S_(a)′BW), and where BW is the effectivebandwidth of readout electronics 32.

FIG. 10 a is a graph of the TNER vs. the normalized excitation frequencyfor different γ (gamma) factors and typical parameters 190, inaccordance with an exemplary embodiment of the present invention.

FIG. 10 b is a graph of the TNER vs. the normalized excitation frequencyfor different ζ_(x) (zeta) factors and typical parameters 200, inaccordance with an exemplary embodiment of the present invention. Theexcitation frequency is normalized by the output natural frequency.Since the excitation frequency is the excitation natural frequency, aswas discussed in section Principle of Operation and Dynamic Model of aSingle Axis De-coupled Mode Rate Gyroscope, FIGS. 10 a and 10 b actuallyillustrate the dependency of the TNER on the deviation between the twonatural frequencies. It is assumed that excitation amplitude 170 can bemaintained constant in the discussed frequency range. Since excitationamplitude 170 is quite limited around the natural frequency, this can beachieved by only a slight change in the applied force of excitationamplitude 170.

Several conclusions can be derived from FIG. 10 a and FIG. 10 b:

-   (1)A resolution of few deg/hr is easily achievable using moderate    damping ratios (10⁻³–10⁻⁴), moderate excitation amplitude (˜1 μm)    and a deviation of a few percent between the natural frequencies.    More demanding requirements (i.e. ζ_(x)˜10⁻⁵, δz˜10 μm,    ω_(nx)=ω_(nz)) results in a TNER<0.1[deg/hr/√Hz].-   (2)At the output natural frequency the dominant noise source is the    thermal mechanical noise.-   (3)The best TNER is achieved at ω=ω_(nz)=ω_(nx), i.e. at zero    deviation between the natural frequencies, where

$\begin{matrix}{S_{\Omega} = {❘_{\omega = {\omega_{n\; x} = {\omega_{n\; z} = \omega_{o}}}}{= {\frac{1}{{{\delta\;\overset{\sim}{z}}}^{2}}\lbrack {{\frac{q\;\gamma}{PR}\zeta_{x}^{2}\omega_{n\;}^{2}} + \frac{2\; k_{B}T\;\zeta_{x}}{m_{{sen}\;}\omega_{n}}} \rbrack}}}} & (22)\end{matrix}$

-   (4)Lowering the γ factor does not improve the best TNER, but reduces    the sensitivity to the deviation between the natural frequencies.    While for high γ factor (˜10000 μm²) the TNER degrades by two orders    of magnitude for a 3–4% deviation, for low γ factor (˜10 μm²) the    TNER is reduced only by a factor of 4–5 for the same deviation. This    reduces the sensitivity to fabrication tolerances and allows better    control on the deviation and bandwidth.

The first term in equation (22), which is related to the photocurrentnoise, increases with the natural frequency. The second term, which isrelated to the thermal mechanical noise, decreases with the naturalfrequency. This may imply an optimal natural frequency for the TNER at

$\omega_{n} = \sqrt[3]{\frac{k_{B}T}{q}\frac{1}{\zeta_{x}m_{{sen}\;}}\frac{PR}{\gamma}}$

Nevertheless, it should be noted that the last is true when maintainingthe excitation amplitude constant over the entire range. This of coursecan be done at the expense of applied force 170.

FIG. 10 c is a graph of the TNER from equation (22) vs. the naturalfrequency for a constant excitation amplitude 210, in accordance with anexemplary embodiment of the present invention. It can be seen that asthe γ factor or the damping ratio ζ_(x), are decreased, the optimal TNERis improved, but shifted to higher natural frequencies. Moreover, it isseen that below the optimal natural frequency, the TNER isthermal-mechanical noise dominated, while above it the TNER isphoto-current noise dominated.

Design Case Study of a Rate-Gyroscope Employing EMIDOS

The TNER and natural frequencies are derived for the structure and thedesign considerations of the rate-gyroscope are now discussed.

A schematic illustration of the rate-gyroscope 220 is shown in FIG. 11,in accordance with an exemplary embodiment of the present invention. Thesuspending beams and the grid are assumed with rectangularcross-section, as described hereinbelow in the discussion of thefabrication process. The total thickness of the rate-gyroscopemechanical structure, i.e. beams, proof-mass 24 and grid 44, is denotedby T. Grid 44 is centered with respect to the inner proof-mass.

Table II summarizes the design parameters for the rate-gyroscope.

TABLE II Parameter Value Total structure length - L_(t) [μm] 2800 Totalstructure width - W_(t) [μm] 1700 Structure thickness - T [μm] 50Excitation frame width - W_(me) [μm] 100 Grid length and width - L_(G)[μm] 525 Grid period - W_(P) [μm] 50 Photodiodes nominal width - W_(D)[μm] 2.5 General spacing - Ws [μm] 10 Comb Drive support length - L_(cs)[μm] 1665 Comb Drive support width - W_(cs) [μm] 50 Comb Drive teethlength - L_(ct) [μm] 100 Comb Drive teeth width - W_(ct) [μm] 5 Youngmodulus - E [Pa] 1.31 × 10¹¹    Mass density- ρ[Kg/m³] 2.33 × 10³   Electron charge - q [Coulomb]  1.6 × 10⁻¹⁹ Illumination source power - P[Watt] 10⁻³ Photodiodes responsivity - R [A/W] 0.2 Thermal energy -k_(B)T [eV] 0.026

FIGS. 12 a, 12 b and 12 c are the dimension design charts for therate-gyroscope, in accordance with an exemplary embodiment of thepresent invention. FIGS. 12 a and 12 b graphically illustrate thecalculated length of the pairs of suspensions vs. the required naturalfrequency for several suspensions widths 226.

FIG. 12 a is the output sensing mode suspensions length vs. the requirednatural frequency 230 for several suspension widths.

FIG. 12 b is the excitation mode suspensions length vs. the requirednatural frequency 240 for several suspension widths.

FIG. 12 c is a graphical representation of the TNER of therate-gyroscope at no-split vs. the natural frequency 250. These threeaccelerometer design charts in combination with TABLE II can be used forsetting the dimensions of the designed rate-gyroscope for preferredTNER. The bold dots 232 in FIGS. 12 a and 12 b are finite-elementsresults of the natural frequencies, which are also summarized in TABLEIII. FIG. 12 c shows results for several values 252 of normalizeddamping coefficient ζ. TABLE II summarizes the set of parameters used inthese calculations. FIG. 12 c presents the calculated TNER for zerosplit vs. the natural frequency for the discussed case study. The threefigures can be used as design charts for the gyro by choosing thenatural frequency from FIG. 12 c and the suspensions dimensions fromFIGS. 12 a and 12 b.

FIG. 13 a is a schematic illustration of the first of three modes of therate-gyroscope case study derived from finite element results, i.e., theoutput sensing mode 260, in accordance with an exemplary embodiment ofthe present invention.

FIG. 13 b is a schematic illustration of the second of three modes ofthe rate-gyroscope case study derived from finite element results, i.e.,the excitation mode 270, in accordance with an exemplary embodiment ofthe present invention.

FIG. 13 c is a schematic illustration of the third of three modes 280 ofthe rate-gyroscope case study derived from finite element results, i.e.,with typical natural frequency at least 5 times higher than either thesensing mode or the excitation mode, in accordance with an exemplaryembodiment of the present invention.

In order to confirm the lumped model of the rate-gyroscope and theassumptions used in the derivations, finite elements (FEM) analysis wasperformed for several structures. The first two main modes of the gyro,the sensing mode and output mode, which were derived from the FEManalysis, are exhibited in FIGS. 13 a and 13 b, confirm the discussionabove on the sensing mode and excitation mode. The third mode in FIG. 13c shows a typical natural frequency at least 5 times higher than themain modes. The FEM results are exhibited as data points 232 in FIGS. 12a and 12 b, showing very good correlation with the lumped model andassumptions. In order to more quantitatively estimate the relativeerror, the FEM results are summarized in TABLE III showing an averageerror less than 2%. The upper part of TABLE III labeled (a), correspondsto the output mode of FIGS. 12 a and 13 a, while the lower part of TABLEIII labeled (b), corresponds to the output mode of FIGS. 12 b and 13 b.The more important positive result is the % split between the naturalfrequencies, which is also calculated in TABLE III, and shows the sameaverage. Thus, the analytical model can be used as a good starting pointfor calculating the design dimensions, and any refinement can be doneusing FEM analysis, if required.

TABLE III f_(n) f_(ne) f_(no) f_(ne) f_(no) L_(ko) L_(ke) (lumped) (FEM)(FEM) error error Split [μm] [μm] [Hz] [Hz] [Hz] (%) (%) (%) (a) 587.3534.8 1000 994.7 1000.4 0.53 0.04 0.57 369.5 336.2 2000 1995.7 2010.50.21 0.53 0.74 281.9 256.4 3000 2995.5 3042.1 0.15 1.40 1.56 232.6 211.54000 4006.5 4099.2 0.16 2.48 2.31 200.4 182.2 5000 5054.8 5117.4 1.102.35 1.24 177.5 161.4 6000 6041.2 6296.3 0.69 4.94 4.22 160.1 145.6 70007201.0 7336.7 2.87 4.81 1.88 146.5 133.2 8000 8167.7 8372.1 2.10 4.652.50 (b) 742.7 675.5 2000 1974.7 1989.3 1.26 0.53 0.74 566.0 514.5 30002953.0 2981.0 1.57 0.63 0.95 466.9 424.3 4000 3938.7 3990.0 1.53 0.251.30 402.2 365.4 5000 4917.0 4993.1 1.66 0.14 1.55 356.0 323.4 60005897.2 6004.8 1.71 0.08 1.82 321.1 291.7 7000 6883.1 6995.2 1.67 0.071.63 293.7 266.8 8000 7458.6 7835.4 6.77 2.06 5.05

Another issue the rate-gyroscope design is the relation between theexcitation amplitude and applied voltage. In the current comb-driveconfiguration the common electrode, i.e. the gyroscope structure, isconnected to a DC voltage V_(DC). The fixed electrodes are connected toan AC voltage, V_(AC), with a 180° phase shift. Thus, the effectiveexcitation force acting on excitation mass is given by

$\begin{matrix}\begin{matrix}{F_{eff} = {{\frac{n_{c}ɛ_{0}T}{W_{c\; t}}( {V_{D\; C} + V_{A\; C}} )^{2}} - {\frac{n_{c}ɛ_{0}T}{W_{c\; t}}( {V_{D\; C} - V_{A\; C}} )^{2}}}} \\{= {4\frac{n_{c}ɛ_{0}T}{W_{c\; t}}V_{D\; C}V_{A\; C}}} \\{\cong {\frac{ɛ_{0}T\; L_{cs}}{W_{c\; t}^{2}}V_{D\; C}V_{A\; C}}}\end{matrix} & (25)\end{matrix}$where n_(c) is the number of fingers in each comb and ε₀ is thedielectric constant of the vacuum. Thus, the excitation force isapproximately independent of the excitation motion and linear with theapplied AC voltage. The DC voltage can be used to control the excitationamplitude in closed loop and the frequency of the AC voltage to lock theexcitation frequency at the natural frequency.

Assuming that the excitation frequency is locked at the excitationnatural frequency, the excitation amplitude is given by,

$\begin{matrix}{{\delta\; z} = {\frac{ɛ_{0}T\; L_{cs}}{2W_{c\; t}^{2}\zeta_{z}{\omega_{n}^{2}( {m_{sen} + m_{exc}} )}}V_{D\; C}V_{A\; C}}} & (26)\end{matrix}$For the typical values in TABLE II and assuming |V_(AC)|=5[V],ζ_(z)=10⁻⁴ and f_(n)=2000[Hz], the amplitude per 1[V] DC is 8.67[μm].Thus, the amplitudes used in the calculations are easily achieved in thediscussed frequency range using only several volts of excitation.

Fabrication Process

In order to achieve good dimensional control and electrical isolationbetween several electrodes at the mechanical structure level, as wasrequired by the rate-gyroscope design, a fabrication process employingsilicon on insulator (SOI) and deep reactive ion etching (DRIE) wasdeveloped. The process flow is shown in FIG. 13 and includes threephotolithography steps.

The process starts with an SOI wafer with an upper p⁺⁺ silicon layer,provided by BCO Technologies, for example. The first lithography definesthe electrical conductors on an evaporated aluminum layer. The secondlithography defines the openings in the upper silicon wafer followed bya DRIE step. The third lithography step defines the openings in thehandle, i.e., lower silicon wafer, using backside alignment, and isfollowed by a second DRIE step. The backside opening provides an opticalpath to the illumination. Hydro fluoride acid (HF) solution is used inthe last step to remove the leftover oxides, thereby releasing thestructure. The mechanical structure is then separated from the wafer andflip-chip bonded. Using the indium bumps technology, bonding isaccomplished to the CMOS chip containing the photodiodes and readoutelectronics. The grid, described hereinabove, is used to align thestructure with the photodiodes.

FIG. 14 is a schematic illustration of the fabrication process 290 ofthe inertial-sensors comprising the following steps: (a) silicon oninsulator (SOI) starting wafer; (b) metal evaporation and patterning;(c) upper silicon patterning using deep reactive ion etching (DRIE); (d)handle silicon patterning and (e) device release using HF wet etching ofremaining SiO₂, in accordance with an exemplary embodiment of thepresent invention.

Illumination Power Fluctuations and Noise

In the analysis of the noise sources, provided hereinabove in thesensing the description of the setup apparatus, the illumination poweris assumed to be constant and to have infinite time coherence. Thus, thenoise contributed by the photocurrent is assumed to be only due to thestatistical behavior of the photons capture in the photodiodes. Sincethe power of all the illumination sources cannot be assumed constant,and the illumination power is actually fluctuating in time, this maycontribute another noise source to the micro-system.

The nature of the power fluctuations of the illumination source ishighly dependent on the type of illumination source. In lasers this isattributable to spontaneous emission. In black bodies and LED's agaussian form for distribution of the electromagnetic field can beassumed. It was shown that for illumination in the visible light andnear infrared, these contributions due to the fluctuations in theillumination power are negligible.

In order to confirm the analysis of the illumination power, thephotocurrent noise is measured for several values of illumination power,using the specific LED to be used in the microsystem. The results areshown in FIG. 15, showing very good correlation with the 2qI_(L)assumption, and confirming that the illumination power fluctuations areindeed negligible.

FIG. 15 is a graphical representation of the measured photocurrent noisespectral density vs. photocurrent 300 for different illumination powers310 provided by a red light emitting diode (LED) used in themicrosystem, in accordance with an exemplary embodiment of the presentinvention.

Photodiodes Responsivity

Another issue regarding the photodiodes is the dependence of theresponsivity upon their width. In order to characterize this effect,photodiodes with several widths are fabricated using Orbit□ 2 μm processprovided by MOSIS. The spectral response of the photodiodes is recordedin the range of 600[nm] to 900[nm] and is exhibited in FIG. 16. Thefluctuations are due to the febry-perot effect attributed to the oxidesabove the photodiodes. The figure shows that the responsivity of thephotodiode is reduced as the width is reduced. This is due to thereduced charge collection by the junction, which covers less spatialarea under the surface. The responsivity is within the range of 0.1–0.4[A/W], depending on the wavelength, which satisfies the abovecalculations and estimations fairly well. Some correcting factor can beused for the responsivity, but due to the weak dependency observed fromFIG. 16, this dependency can be neglected.

FIG. 16 is a graphical representation of the measured spectral responsesof photodiodes 310 with different optical window widths 312. Thephotodiodes are fabricated in a standard CMOS process provided by Orbit□via the MOSIS project, in accordance with an exemplary embodiment of thepresent invention.

Diffraction Effects

Also to be considered is the effect of diffraction on the performance ofthe E-MIDOS, and sensor performance. Since the grid slits are long andnarrow, the effect of diffraction can be estimated by using a twodimensional model. The first dimension is the along the motion, or theslit width, i.e. the x-direction. The second dimension is along theillumination propagation path between the grid and the photodiodes,which is denoted as the z-direction.

The diffraction pattern can be approximated by assuming that the gridacts like a mask to the illumination propagation. Then, after ittraverses the mask, the illumination is disassembled into its basicplane waves, using the Fourier transform. The propagation of each of theplane waves along the z-axis is summed at the required z-plane, yieldingthe diffraction pattern, i.e.f(x,z)=F ⁻¹ {F{f(x,0)}×exp(iz√{square root over (K ⁰ ² −K _(x) ²)})}  (27)where F{ }, F⁻¹{ } are the Fourier and inverse Fourier transforms,respectively, k_(x) is the wave vector along the x-axis and k₀=2π/λ,where λ is the illumination wavelength. The total power falling on thephotodiodes is then given by

$\begin{matrix}{P = {\int_{{- W_{D}} + x}^{W_{D} + x}{{{f( {x,z} )}}^{2}\ {\mathbb{d}x}}}} & (28)\end{matrix}$and the photocurrent is directly proportional to it.

FIG. 17 a is a graphical representation of the effect of diffraction onthe sensing of the displacement using EMIDOS 320, showing thediffraction patterns at the photodiodes plane for various distances 322,dz, between the grid and photodiodes, in accordance with an exemplaryembodiment of the present invention.

That is, FIG. 17 a presents the illumination diffraction pattern atseveral z-planes for the parameters used in the design of the sensors asshown hereinabove in TABLE I AND TABLE II. For z-planes further awayfrom the grid, the diffraction pattern becomes less constant, andapparently deviates more from the optical approximations of therays-optics.

FIG. 17 b is a graphical representation of the effect of diffraction onthe sensing of the displacement using EMIDOS 330, showing thedifferential response of the photodiodes taking into account thediffraction pattern vs. the grid displacement dx, and exhibiting verygood linearity at small displacements with only slight non-linearity atlarge dz's 322 and large displacements of the grid dx, in accordancewith an exemplary embodiment of the present invention.

Since the diffraction pattern itself does not explain all the phenomena,the power difference between the two photodiode grids is calculatedusing equation (28) and is exhibited in FIG. 17 b. This surprisinglyshows that even though a diffraction pattern may be far different fromthe simple rays optic distribution, the integral of the illumination isquite linear with the displacement, with only a slight divergence fromlinearity for very large displacements. The only real difference foremail displacements is the actual slope, which may be changed slightlydue to the diffraction effect. Thus, the approxiations used in theperformance estimations are justified, with only a slight correction,which can be compensated for by the illumination power used. Regardingthe linearity, it is clearly seen that good linearity is expected.

Having described the invention with regard to certain specificembodiments thereof, it is to be understood that the description is notmeant as a limitation, since further modifications may now suggestthemselves to those skilled in the art, and it is intended to cover suchmodifications as fall within the scope of the appended claims.

1. A micro-opto-electro-mechanical system for measuring the accelerationof a platform along a fixed axis, using partially integrated modeenhanced modulated integrative differential optical sensing, said systemcomprising: a CMOS chip comprising at least two integrated arrays ofphotodiode illumination detectors and analog readout electronics; aframe affixed to said CMOS chip; an LED mounted above said frame,providing illumination for said photodiode detectors; a sensingproof-mass, elastically suspended by a set of beams fixed to said frame;a grid of slits integrally formed with said sensing proof-mass, andbeing orthogonal to said fixed acceleration axis, such that when saidsystem is at rest, said grid evenly and partially covers each of saidarrays of photodiode detectors, so that equal amounts of lightilluminate each of said arrays and equal photocurrents are measured ateach of said arrays, and when said platform accelerates, said sensingproof-mass is displaced along said fixed acceleration axis, therebyincreasing the exposed area of one of said arrays of photodiodedetectors to illumination, while decreasing the exposed area of anotherone of said arrays of photodiode detectors, and increasing a resultingdifferential photocurrent from said arrays of photodiode detectors, saiddifferential photocurrent being proportional to the displacement of saidsensing proof-mass and therefore to the acceleration, thus providing ameasurement of the acceleration of said platform.
 2. A system accordingto claim 1, wherein said micro-opto-electro-mechanical system ismass-produced.
 3. A system according to claim 1, further comprising asecond grid of slits and at least two additional arrays of photodiodes,wherein said at least two additional arrays of photodiodes and saidsecond grid of slits are orthogonal to each other for measuringacceleration along multiple axes.
 4. A system according to claim 1,wherein said analog readout electronics comprises: an amplificationstage for each of said arrays of photodiode detectors; and a subtractionstage.
 5. A micro-opto-electro-mechanical system for measuring theacceleration of a platform along a fixed axis using fully integratedmode enhanced modulated integrative differential optical sensing, saidsystem comprising: a CMOS chip comprising at least two integrated arraysof photodiode illumination detectors and analog readout electronics; aframe affixed to said CMOS chip; an LED mounted above said frame,providing illumination for said photodiode detectors; a sensingproof-mass, elastically suspended by a set of beams fixed to said frame;a first grid of slits integrally formed with said sensing proof-mass,and being orthogonal to said acceleration axis; a second grid of slitsfixed to said frame, and centered with said first grid of slits, suchthat when said system is at rest, said first and second grid of slitsare evenly and fully exposed to each of said arrays and photocurrentsare measured at each of said arrays, and when said platform accelerates,said sensing proof-mass is displaced along said fixed acceleration axis,and said first grid is displaced with respect to said second grid,thereby increasing the gap on one side between said first and secondgrid of slits and therefore increasing the exposed area of one of saidarrays of photodiode detectors to illumination, while decreasing the gapon the other side between said first and second grid of slits andtherefore decreasing the exposed area of another one of said arrays ofphotodiode detectors, and increasing a resulting differentialphotocurrent from said arrays of photodiode detectors, said differentialphotocurrent being proportional to the displacement of said sensingproof-mass and therefore to the acceleration, thus providing ameasurement of the acceleration of said platform.
 6. A system accordingto claim 5, wherein said micro-opto-electro-mechanical system ismass-produced.
 7. A system according to claim 5, further comprising atleast two additional arrays of photodiodes, wherein said at least twoadditional arrays of photodiodes and said second grid of slits areorthogonal to each other for measuring acceleration along multiple axes.8. A system according to claim 5, wherein said analog readoutelectronics comprises: an amplification stage for each of said arrays ofphotodiode detectors; and a subtraction stage.
 9. Amicro-opto-electro-mechanical system for measuring the rate of rotationof a platform about a fixed axis thereof using partially integrated modeenhanced modulated integrative differential optical sensing, said systemcomprising: a CMOS chip comprising at least two integrated arrays ofphotodiode illumination detectors and analog readout electronics; aframe attached to said CMOS chip; an LED mounted above said frame,providing illumination for said photodiode detectors; a excitation mass,elastically suspended by a set of beams fixed to said frame, such thatsaid excitation mass is allowed to move along excitation axis, and saidexcitation axis is orthogonal to said rate of rotation axis; a sensingproof-mass, elastically suspended to said excitation mass by a secondset of beams, such that sensing proof-mass is allowed to move alongsensing axis, and said sensing axis is orthogonal to said excitationaxis and said rate of rotation axis; a grid of slits integrally formedwith said sensing proof-mass, and being orthogonal to said sensing axis,such that when said system is at rest, said grid evenly and partiallycovers each of said arrays of photodiode detectors, so that equalamounts of light illuminate each of said arrays and equal photocurrentsare measured at each of said arrays, and when mechanical vibration isapplied along said excitation axis and said platform rotates about saidrate of rotation axis, said sensing proof-mass is displaced along saidsensing axis due to Coriolis forces, thereby increasing the exposed areaof one of said arrays of photodiode detectors to illumination whiledecreasing the exposed area of another one of said arrays of photodiodedetectors to illumination, and increasing a resulting differentialphotocurrent from said arrays of photodiode detectors, said differentialphotocurrent being proportional to the displacement of said sensingproof-mass and therefore to the rate of rotation, thus providing ameasurement of the rate of rotation of said platform.
 10. A systemaccording to claim 9, wherein said micro-opto-electro-mechanical systemis mass-produced.
 11. A system according to claim 9, further comprisinga second grid of slits and at least two additional arrays ofphotodiodes, wherein said at least two additional arrays of photodiodesand said second grid of slits comprise multiple arrays and gridsorthogonal to each other for measuring the rate of rotation aboutmultiple axes.
 12. A system according to claim 9, wherein said analogreadout electronics comprises: an amplification stage for each of saidarrays of photodiode detectors; and a subtraction stage.
 13. A systemaccording to claim 9, wherein said mechanical vibration results fromelectrostatic actuation.
 14. A system according to claim 9, wherein saidmechanical vibration results from magnetostatic actuation.
 15. A systemaccording to claim 9, wherein said mechanical vibration results frompiezoelectric actuation.
 16. A system according to claim 9, wherein saidmechanical vibration results from thermal actuation.
 17. Amicro-opto-electro-mechanical system for measuring the rate of rotationof a platform about a fixed axis thereof using fully integrated modeenhanced modulated integrative differential optical sensing, said systemcomprising: a CMOS chip comprising at least two integrated arrays ofphotodiode illumination detectors and analog readout electronics; aframe attached to said CMOS chip; an LED mounted above said frame,providing illumination for said photodiode detectors; an excitationmass, elastically suspended by a set of beams fixed to said frame, suchthat said excitation mass is allowed to move along an excitation axis,and said excitation axis is orthogonal to said rate of rotation axis; asensing proof-mass, elastically suspended to said excitation mass by asecond set of beams, such that sensing proof-mass is allowed to movealong a sensing axis, and said sensing axis is orthogonal to saidexcitation axis and said rate of rotation axis; a first grid of slitsintegrally formed with said sensing proof-mass, and being orthogonal tosaid sensing axis; a second grid of slits fixed to said frame, andcentered with said first grid of slits, such that when said system is atrest, said first and second grid of slits are evenly and fully exposedto each of said arrays of photodiode detectors, so an even amount oflight illuminating each of said arrays and a photocurrent is measured ateach of said arrays, and when mechanical vibration is applied along saidexcitation axis and said platform rotates about said rate of rotationaxis, said sensing proof-mass is displaced along said sensing axis dueto Coriolis forces and said first grid is displaced with respect to saidsecond fixed grid, thereby increasing the gap on one side between saidfirst and second grid of slits and therefore increasing the exposed areaof one of said arrays of photodiode detectors to illumination anddecreasing the gap on the other side between said first and second gridof slits and therefore decreasing the exposed area of another one ofsaid arrays of photodiode detectors, and increasing a resultingdifferential photocurrent from said arrays of photodiode detectors, saiddifferential photocurrent being proportional to the displacement of saidsensing proof-mass and therefore to the rate of rotation, thus providinga measurement of the rate of rotation of said platform.
 18. A systemaccording to claim 17, wherein said micro-opto-electro-mechanical systemis mass-produced.
 19. A system according to claim 17, further comprisingat least two additional arrays of photodiodes, wherein said at least twoadditional arrays of photodiodes and said second grid of slits comprisemultiple arrays and grids orthogonal to each other for measuring therate of rotation about multiple axes.
 20. A system according to claim17, wherein said analog readout electronics comprises: an amplificationstage for each of said arrays of photodiode detectors; and a subtractionstage.
 21. A system according to claim 17, wherein said mechanicalvibration results from electrostatic actuation.
 22. A system accordingto claim 17, wherein said mechanical vibration results frommagnetostatic actuation.
 23. A system according to claim 17, whereinsaid mechanical vibration results from piezoelectric actuation.
 24. Asystem according to claim 17, wherein said mechanical vibration resultsfrom thermal actuation.
 25. A partially integrated modeenhanced-modulated-integrative-differential-optical-sensing apparatusfor measuring displacement along a given axis, said apparatuscomprising: a CMOS chip comprising at least two integrated arrays ofphotodiode illumination detectors and analog readout electronics; aframe affixed to said CMOS chip; an LED mounted above said frame,providing illumination for said photodiode detectors; a sensingproof-mass, elastically suspended by a set of beams fixed to said frame;a grid of slits integrally formed with said sensing proof-mass, andbeing orthogonal to said given displacement axis, such that when saidsystem is at rest, said grid evenly and partially covers each saidarrays of photodiode detectors, so that equal amounts of lightilluminate each of said arrays and equal photocurrents are measured ateach of said arrays, and when said sensing proof-mass is displaced alongsaid given displacement axis, the exposed area to illumination of one ofsaid arrays of photodiode detectors is increased and the exposed area ofanother one of said arrays of photodiode detectors is decreased, suchthat a resulting differential photocurrent from said arrays ofphotodiodes is increased, said differential photocurrent beingproportional to the displacement of said sensing proof-mass, thusmeasuring the displacement of said apparatus.
 26. A fully integratedmode enhanced-modulated-integrative differential-optical-sensingapparatus for measuring displacement along a given axis, said apparatuscomprising: a CMOS chip comprising at least two integrated arrays ofphotodiode illumination detectors and analog readout electronics; aframe affixed to said CMOS chip; an LED mounted above said frame,providing illumination for said photodiode detectors; a sensingproof-mass, elastically suspended by a set of beams fixed to said frame;a first grid of slits integrally formed with said sensing proof-mass,and being orthogonal to said given displacement axis; a second grid ofslits fixed to said frame, and centered with said first grid of slits,such that when said system is at rest, said first and second grid ofslits are evenly and fully exposed to each of said arrays of photodiodedetectors, so that equal amounts of light illuminate each of said arraysand equal photocurrents are measured at each of said arrays, and whensaid sensing proof-mass is displaced along said given displacement axis,and said first grid is displaced with respect to said second fixed grid,thereby increasing the gap on one side between said first and secondgrid of slits and therefore increasing the exposed area of one of saidarrays of photodiode detectors to illumination and decreasing the gap onthe other side between said first and second grid of slits and thereforedecreasing the exposed area of another one of said arrays of photodiodedetectors, such that a resulting differential photocurrent from saidarrays of photodiode detectors is increased, said differentialphotocurrent being proportional to the displacement of said sensingproof-mass; thus measuring the displacement of said apparatus.